If f(x) = x

^{4}- kx^{2}- 6x + 7 has a remainder of 22 when divided by x+2; find k.

__solution__
f(x) = x

^{4}- kx^{2}- 6x + 7
x + 2 = 0

x = -2

f(x) = (-2)

^{4}- k(-2)^{2}- 6(-2) + 7 = 22
16 - 4k + 12 + 7 = 22

16 - 4k + 19 = 22

16 + 19 = 22 + 4k

16 + 19 - 22=4k

35 - 22=4k

13 = 4k

k =

^{13}/4 after dividing by 4 both sides.
hence k=

^{13}/4

__TRY THIS......................__^{4}- kx

^{2}- 5x - 31 has a remainder of 18 when divided by x-2; find k.